Question

A cylindrical container is to be made of tin sheet. The height of the container is 1 m and its diameter is 70cm.If the container is open at the top and the sheet costs ₹300 per m2 , find the cost of the tin sheet for making the container

Answer 1

Gɪᴠᴇɴ :-

• Cylinder container is made of tin sheet
• Container is open at the top and the sheet costs ₹300 per m²
• Height of the container = 1m
• Diameter of container = 70cm
• Radius of container = 70/100 × 2 = 0.35 m

ᴛᴏ ғɪɴᴅ :-

• The cost of the tin sheet for making the container

sᴏʟᴜᴛɪᴏɴ :-

☞As we know that

✚ Total surface area of cylinder

→ Curved surface area of cylinder + area of two circles

→ 2πrh + 2πr²

• Container is open at the top.

✚ So, area of container

➪ 2πrh + πr²

➪ 2 × 22/7 × 0.35 × 1 + 22/7 × 0.35 × 0.35

➪ 2 × 22 × 0.05 + 22 × 0.05 × 0.35

➪ 44 × 0.05 + 0.385

➪ 2.2 + 0.385

➪ 2.585 m²

• Therefore, the area of the tin sheet for making the container is 2.585m²

✚ Now, the cost of the tin sheet for making the container

• Cost of 1m² sheet = Rs.300

➪ 2.585 × 300

➪ Rs.775.5

Hence,

• The cost of the tin sheet is Rs.775.5

Answer 2

Given :-

• The height (h) of the container is 1m. and it's diameter (d) is 70cm. The container is open at the top and the sheet costs ₹300 per m².

To Find :-

• The cost of the tin sheet for making the container.

Solution :-

____________________

• Diameter (d) = 70cm

=> r = d/2

=> r = 70/2

=> r = 35cm.

=> r = 35/100 m

=> r = 0.35 m.

____________________

Now,

• Area of tin sheet required = Curved surface area of cylinder + Area of base

=> Area of tin sheet required = 2πrh + πr²

=> Area of tin sheet required = 2×22/7× 0.35 ×1 + 22/7 × (0.35)²

=> Area of tin sheet required = 44 × 0.05 × 1 + 22/7 × 0.1225

=> Area of tin sheet required = 2.2 + 0.385

=> Area of tin sheet required = 2.585m².

____________________

• The cost of tin sheet for making container = 2.585m² × ₹300/m²

=> The cost of tin sheet for making container = ₹775.5 .

Hence,

• The cost of tin sheet for making container is ₹775.5.